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In this paper we present the Amharic Speech Emotion Dataset (ASED), which covers four dialects (Gojjam, Wollo, Shewa and Gonder) and five different emotions (neutral, fearful, happy, sad and angry). We believe it is the first Speech Emotion Recognition (SER) dataset for the Amharic language. 65 volunteer participants, all native speakers, recorded 2,474 sound samples, two to four seconds in length. Eight judges assigned emotions to the samples with high agreement level (Fleiss kappa = 0.8). The resulting dataset is freely available for download. Next, we developed a four-layer variant of the well-known VGG model which we call VGGb. Three experiments were then carried out using VGGb for SER, using ASED. First, we investigated whether Mel-spectrogram features or Mel-frequency Cepstral coefficient (MFCC) features work best for Amharic. This was done by training two VGGb SER models on ASED, one using Mel-spectrograms and the other using MFCC. Four forms of training were tried, standard cross-validation, and three variants based on sentences, dialects and speaker groups. Thus, a sentence used for training would not be used for testing, and the same for a dialect and speaker group. The conclusion was that MFCC features are superior under all four training schemes. MFCC was therefore adopted for Experiment 2, where VGGb and three other existing models were compared on ASED: RESNet50, Alex-Net and LSTM. VGGb was found to have very good accuracy (90.73%) as well as the fastest training time. In Experiment 3, the performance of VGGb was compared when trained on two existing SER datasets, RAVDESS (English) and EMO-DB (German) as well as on ASED (Amharic). Results are comparable across these languages, with ASED being the highest. This suggests that VGGb can be successfully applied to other languages. We hope that ASED will encourage researchers to experiment with other models for Amharic SER.